On the different Theories of Jrdies, Faults, &c. 413 



friction ; and they arc auxiliaries in any case not too great 

 to be allowed. But Dr. Charles Hutton seems to contro- 

 vert this opinion, or fact, of Boiiguer ; for in a letter 

 (Monthly Magazine, August lSO-2, vof. xiv. p. 27) he says, 

 "The old theory (viz. that of De la Hire, &c.) so violently 

 contended for, can have no place in the practice of arch 

 buildinar, because that here the arch stones cannot act as 

 true mathematical v.edges. For in these it is well known 

 that they are retained in their places or have their weight 

 and other forces acting on their back balanced bv two 

 forces acting perpendicularly against their sides, which are 

 conceived to be perfectly smooth or polished. But will it 

 be said that this is the case'with the voussoirs or wedges of 

 a stone arch ? Are their sides polished, or quite void of 

 friction ? &c," 



In his first memoir M. Couplet gives a geometrical mode 

 of determining the extrados of a circular vault, which may 

 be inserted to show the identity of the theory with that of 

 Dc la Hire and M. Parent. 



Upon vc (fig. 3) as a diameter describe the arc vd, cut- 

 ting the intrados at d, and draw dz perpendicular to and 

 cutting vc in s. DiAwJk, so that hit = vs, which expresses 

 the weight of 'he voussoir A. To find Ini of the voussoir B, 

 make az = gf, which expresses the weight of the vaussoir 

 B. Upon cz as a diameter describe an arc, cutting vy a. 

 tangent to the vertex in i/. Make Ic — yc, hence Lin' re- 

 quired. If the back of the voussoir B be biseced, the ex- 

 trados of an arch of voussoirs infinitely siifall, will pass 

 through the point of bisection. 



M. Couplet's theory of abutment piers is formed, like 

 that of De la [lire, from the results of the wedi'e and the 

 lever. 



M. Belidor in his ''Science des Ivgenicurs," ] 7^9, investi- 

 gated ihe theory of abutment piers more fully than had 

 i)een before done, also upon the principles of De la Hire. 

 In the volume of the yjcnd. Scien. Par. 1734, M. Bouguer 

 published a memoir upon the curved lines proper to form 

 a dome : he shows that an infinity of curved lines are pro- 

 per to form' domes, and indicates at the same lime the 

 manner of choosing them ; and lastly determines the forn), 

 which is a mechanical curve, of the' last of all the curved 

 lines which i.s proper for a dome: he iias given a table, 

 whereby this curve may be consirncted. His mode of in- 

 ve&Uir:^\'\(m is analogical to the mode of determining the 

 equiii'jr.'ion of the arch of uniform tf)ickncss. 



Mr. 



